Question

Below are data for the number of students in each of four age groups that are enrolled in several local schools:

Age Group	Franklin School	Lowell Public School	JeanneD’arc School	International School
Toddlers (1 – 4 yrs.) Pre-adolescents (5 - 8 yrs.) Adolescents (9 - 12 yrs.) Teens (13 - 18 yrs.)	0 56 131 0	36 52 51 64	0 24 98 111	34 41 52 69

Using the included data file and SPSS, create a separate Pie Chart of the age groups for each school. Which school has the largest percentage of pre-adolescents? Then create of Bar Graph of the total count of students in each age group that are enrolled in local schools (including the local International School). Which age group represents the largest percentage of local students?

Answer 1

The pie chart is a circular statistical graphic which shows you the proportion of different characters / groups / elements in a population. It helps to observe the proportions of the elements or different groups by observing the slices of the circle. The pie chart uses a formula to cut the circle into slices to show the proportion of the groups or a character.

Here in this example, the pie chart shows the proportion of different age groups of students in a local school.

Method :

1. You can calculate the percentage of an age group in a local school using below formula :

Note : As the percentage are calculate out of 100, hence we multiply by 100 in formula of P

Consider, f : Number of students of a particular age group in a local school

N : Total number of students from all age groups in a local school.

P : Proportion of students from an age group in a local school

P = ( f / N ) * 100 ( in percentage out of 100%)

2. You can can make the pie chart using below formula :

Note : As the circle is of 360 degree, so you will have to cut the circle into slices according to it such that if you add the angle of all slices ( from centre of circle,considering one of the two side of slice as reference) the total will be 360 degree and the first slice you can make by taking a line between the centre of circle and any point on circumference and then moving to other slices in clockwise or anti-clockwise direction.

Consider, k : Number of students of a particular age group in a local school

N : Total number of students from all age groups in a local school.

S : Proportion of students from an age group in a local school

S = ( k / N ) * 360 ( in degrees out of 360 degrees)

3. To create bar graph :

i. First calculate the total number of students from each age group and then plot the age groups on X axis and Number of students on Y axis and plot the bar according to it.

ii. As you can see the highest number of students are from the age group Adolescents (9 - 12 yrs.) so this lead to that the age group of Adolescents (9 - 12 yrs.) has largest percentage of local students.Just to be sure, you can use the formula given in the step 1. by taking

f : Total number of students from an age group from all schools and

N : Total number of students from all age grorups from all schools.

The pie chart and bar graph are below :