Excel Output
The data set that will be analyzed in this paper was compiled from the website of the Office for National Statistics (2016). It describes the birth rates in England and Wales over the period that lasted from 1991 to 2015. The data set includes information about the number of babies produced by mothers of different age categories (namely, less than 20 years old, aged 20-24, aged 25-29, aged 30-34, aged 35-39, and those who are 40 or older), and the overall number of children who were born during each year of the period in question.
The descriptive statistics output for the number of live births in England and Wales from 1991 until 2015 is as follows:
The pivot table for the data:
The frequency table for the data is provided next. The frequencies were calculated for the number of years in which the number of live births fell into the categories described in the “Labels” column. The “Bin” column describes the upper limit of a category.
The frequency chart is given next. It presents the same data as was supplied in the frequency table provided above.
Comments and Conclusions
Descriptive Statistics
Therefore, the supplied Excel output allows for interpreting the data pertaining to the number of births of children across the years in England and Wales. In particular, the table of descriptive statistics provides some details related to the distribution of these births across years.
The mean of the data set is a measure of its central tendency; it is simply the arithmetic mean, and it shows which number of babies was produced on average (Remenyi, Onofrei, & English, 2011). Thus, if nearly 666,828.04 babies were born each year over 25 years, the total number of babies produced in this manner would be equal to the total number of babies who were born in England and Wales in 1991-2015.
The standard error of the mean is the standard deviation of the sampling distribution of means (George & Mallery, 2016); in other words, if the analyzed data represented a sample, then other samples drawn from the same population would have a standard deviation equal to 8180.73. However, it is worth remembering that the analyzed data describes the whole population, not a sample.
The median is the middle value of the distribution (George & Mallery, 2016). In some cases, the median might allow for approximately assessing how skewed the data is; for instance, if the median value of the given distribution was, e.g., 710,000, it would be possible to conclude that there are more large values in the data than small values. However, in this case, the median is rather close to the mean, which suggests that the data is not very skewed.
There is no mode (the most frequently occurring value) in the data, for it did not occur that the same number of babies were born in any two (or more) years in England and Wales from 1991 to 2015. If it had happened (which is an event of rather low probability), the distribution would have had a mode. However, on the whole, the model is not an adequate measure of the central tendency of continuous data (Warner, 2013).
The standard deviation of a distribution demonstrates how spread out the values of a variable is (Forthofer, Lee, & Hernandez, 2007). It is most informative when reported along with the mean. In a normally distributed data, approximately 68% of the values of the variable will lie within ± 1 standard deviation from the mean, nearly 95.5% of the values will lie within ± 2 standard deviations from the mean, and nearly 99.7% of the values will lie within ± 3 standard deviations from the mean (George & Mallery, 2016, p. 113).
Therefore, if the number of live births in England and Wales in 1991-2015 is approximately normally distributed, it can be concluded that in nearly two-thirds of the years (that is, in approximately 16 years), the number of births was equal to some numbers inside the interval 666828.04 ± 40903.67494; that is, between 625,924 and 707,732. And in nearly 95% of the years (that is, in roughly 24 years), the number of births was equal to some numbers inside the interval 666828.04 ± 2 * 40903.67494; that is, between 585,020 and 748636. It can be seen from the data that all the numbers fall inside the latter interval, which could easily happen for the given sample size (25).
The variance of the data is equal to the square of the standard deviation. It can also be used to measure the degree of spread of the data, but the standard deviation is often considerably more convenient because it allows for calculating the approximate percentage of the values within desired intervals around the mean (Remenyi et al., 2011).
Kurtosis permits assessing how “peaked” or “flat” a distribution is; that is, whether there are more values close to the mean or whether there are more values far from the mean (Warner, 2013). The negative kurtosis in the given distribution (-1.04) means that there are more values that are far from the mean than in a normal distribution; however, the value of kurtosis is not extreme and may be considered acceptable for most analytical purposes (George & Mallery, 2016, p. 114).
Simultaneously, skewness shows how skewed the data is; in other words, whether there are more values that are larger than the mean than those that are smaller than the mean, or vice versa. A negative skewness means that there are more values larger than the mean than values smaller than the mean. In the given case, the skewness is negative, but its value is very close to zero (-0.23), so the data is almost symmetrical around the mean.
The range represents the difference between the largest and the smallest values of the distribution. It means that during the year in which the number of births was the smallest, 135040 fewer babies were born than during the year in which the number of births was the largest.
The minimum (maximum) value is simply the number of babies that were produced during the year in which the number of births was the smallest (the largest). The values provided for the smallest (1) (largest (1)) also denote the minimum (maximum) values of this distribution.
The sum is the total number of babies born in England and Wales in 1991-2015.
The count is the total number of years the data related to that which was analyzed. In this case, it might be considered the sample size.
The confidence level (95%) statistic shows that the probability is 95% that the mean of the population is equal to the mean of the given sample plus-or-minus the confidence level (that is, 666828.04 ± 16884.20706). However, the number of births is calculated for the whole population of England and Wales, so assessing the mean of the “population” makes sense if it is needed to estimate the number of births in some year other than 1991-2015.
The Pivot Table
The pivot table allows for looking at the data from a number of different angles; for instance, it permits calculating the total amount of units represented in the cells of the data (Jelen & Alexander, 2013). In the given case, the pivot table was utilized to compute the total number of births given by mothers of particular age groups during the period 1991-2015. For instance, it can be seen that a total of 3,191,343 babies were produced by mothers aged 20-24 in 1991-2015. The number of total births (16,670,701) was also calculated in the column “Sum of a number of live births.”
The Frequency Table
The frequency table shows how often it occurred that the number of births fell within the given ranges during the years 1991-2015. For instance, the number of births was between 690,001 and 720,000 seven times during the period in question. The frequency table might allow one to conclude how often the data falls within a certain category.
The Frequency Chart
The provided frequency chart presents the same data as the frequency table, but in a visual manner. This chart also permits one to compare with which relative frequency the data falls into a certain category.
Both frequency charts and frequency tables are most useful when they are utilized for categorical (nominal or ordinal) data, for in these cases, they allow one to see how often the certain values of the data occur in the sample (for instance, how many males and females there are in the sample).
References
Forthofer, R. N., Lee, E. S., & Hernandez, M. (2007). Biostatistics: A guide to design, analysis, and discovery (2nd ed.). Burlington, MA: Elsevier Academic Press.
George, D., & Mallery, P. (2016). IBM SPSS Statistics 23 step by step: A simple guide and reference (14th ed.). New York, NY: Routledge.
Jelen, B., & Alexander, M. (2013). Pivot table data crunching: Microsoft Excel 2010. Upper Saddle River, NJ: Pearson Education.
Office for National Statistics. (2016). Birth summary tables – England and Wales. Web.
Remenyi, D., Onofrei, G., & English, J. (2011). An introduction to statistics using Microsoft Excel. Kidmore End, UK: Academic Publishing Limited.
Warner, R. M. (2013). Applied statistics: From bivariate through multivariate techniques (2nd ed.). Thousand Oaks, CA: SAGE Publications.