Lesson: Learn about Statistics with Nick Pope

Nick Pope

Nick Pope was born on April 19^th, 1992 in Soham Cambridgeshire. He is an English professional footballer who plays as a goalkeeper for Burnley in the Premier League and for England.

Pope started his career in the Ipswich Town youth team but was released when he was sixteen. Following his release by Ipswich, he joined Bury St Edmunds’ local non-league club Bury Town in 2008.

In May 2011, League One club Charlton Athletic signed Pope after he was spotted by scouts during Bury’s 2–1 win over Billericay Town. While at Charlton, he went out on loan to several clubs before making his debut for the Club in May 2013, after which he made 33 appearances. In June 2016, he joined Premier League club, Burnley and has since then has played for them in 64 games.

Pope was called up to the England squad for the first time in March 2018 and was named in the 23-man England squad for the 2018 FIFA World Cup. He made his debut in June 2018 as a 65th-minute substitute as England beat Costa Rica 2–0 in a pre-tournament friendly. Pope made his second international appearance in a 4–0 win against Kosovo for the final game of Euro Qualifying in November 2019.

Statistics

Statistics is the mathematical discipline of collecting, analysing, presenting, and interpreting data. Historically, government requirements for census information, as well as figures for a range of economic activities created the early impetus for the field of statistics.

Data may be classified as either quantitative or qualitative. Quantitative data measure either how much or how many of something, and qualitative data provides labels, or names, for categories of like items. For example, suppose that a particular study is interested in characteristics such as age, gender, marital status, and annual income for a sample of 100 individuals.

The area of descriptive statistics is concerned primarily with methods of presenting and interpreting data using graphs, tables, and numerical summaries. Descriptive statistics are tabular, graphical, and numerical summaries of data. The purpose of descriptive statistics is to allow the presentation and interpretation of data. Most of the statistical presentations we see are descriptive in nature.

Tabular methods

The most commonly used tabular summary of data for a single variable is a frequency distribution. A frequency distribution shows the number of data values in each of several non-overlapping classes. Another tabular summary, called a relative frequency distribution, shows the fraction, or percentage of data values in each class. The most common tabular summary of data for two variables is a cross tabulation.

For a qualitative variable, a frequency distribution shows the number of data values in each qualitative category. For instance, the variable gender has two categories: male and female. Thus, a frequency distribution for gender would have two non-overlapping classes to show the number of males and females. A relative frequency distribution for this variable would show the fraction of individuals that are male and the fraction of individuals that are female.

Constructing a frequency distribution for a quantitative variable requires more care in defining the classes and the division points between adjacent classes. For instance, if the age data of the example above ranged from 22 to 78 years, the following six non-overlapping classes could be used: 20–29, 30–39, 40–49, 50–59, 60–69, and 70–79. A frequency distribution would show the number of data values in each of these classes, and a relative frequency distribution would show the fraction of data values in each.

A cross tabulation is a two-way table with the rows of the table representing the classes of one variable and the columns of the table representing the classes of another variable. To construct a cross tabulation using the variables gender and age, gender could be shown with two rows, male and female, and age could be shown with six columns corresponding to the age classes 20–29, 30–39, 40–49, 50–59, 60–69, and 70–79. The entry in each cell of the table would specify the number of data values with the gender given by the row heading and the age given by the column heading. Such a cross tabulation could be helpful in understanding the relationship between gender and age.

Graphical Methods

A number of graphical methods are available for describing data. A bar graph is a graphical device for depicting qualitative data that have been summarized in a frequency distribution. Labels for the categories of the qualitative variable are shown on the horizontal axis of the graph. A bar above each label is constructed such that the height of each bar is proportional to the number of data values in the category.

Numerical measures

A variety of numerical measures are used to summarise data. The proportion, or percentage of data values in each category is the primary numerical measure for qualitative data. The mean, median, mode, and range are the most commonly used numerical measures for quantitative data.

The mean, often called the average, is computed by adding all the data values for a variable and dividing the sum by the number of data values. The mean is a measure of the central point of the data.

The median is another measure of central location that, unlike the mean, is not affected by extremely large or extremely small data values. When determining the median, the data values are first ranked in order from the smallest value to the largest value. If there is an odd number of data values, the median is the middle value; if there is an even number of data values, the median is the average of the two middle values.

The third measure of central tendency is the mode, the data value that occurs with greatest frequency.

The range is the difference between the largest value and the smallest value, and is the simplest measure of variability in the data. The range is determined by only the two extreme data values.