Answer:
![Range = 17](https://tex.z-dn.net/?f=Range%20%3D%2017)
![Intervals = 5](https://tex.z-dn.net/?f=Intervals%20%3D%205)
![Widt = 4](https://tex.z-dn.net/?f=Widt%20%3D%204)
Step-by-step explanation:
Given
The above data
Solving (a): The range:
![Range = Highest - Least](https://tex.z-dn.net/?f=Range%20%3D%20Highest%20-%20Least)
Where
![Highest = 24](https://tex.z-dn.net/?f=Highest%20%3D%2024)
![Least = 7](https://tex.z-dn.net/?f=Least%20%3D%207)
So:
![Range = 24 - 7](https://tex.z-dn.net/?f=Range%20%3D%2024%20-%207)
![Range = 17](https://tex.z-dn.net/?f=Range%20%3D%2017)
Solving (b): Number of intervals.
From the given data:
![n = 25](https://tex.z-dn.net/?f=n%20%3D%2025)
![Intervals = \sqrt n](https://tex.z-dn.net/?f=Intervals%20%3D%20%5Csqrt%20n)
![Intervals = \sqrt {25](https://tex.z-dn.net/?f=Intervals%20%3D%20%5Csqrt%20%7B25)
![Intervals = 5](https://tex.z-dn.net/?f=Intervals%20%3D%205)
Solving (c): Interval width
This is calculated as:
![Width = \frac{Range}{Intervals}](https://tex.z-dn.net/?f=Width%20%3D%20%5Cfrac%7BRange%7D%7BIntervals%7D)
![Width = \frac{17}{5}](https://tex.z-dn.net/?f=Width%20%3D%20%5Cfrac%7B17%7D%7B5%7D)
![Width = 3.4](https://tex.z-dn.net/?f=Width%20%3D%203.4)
--- round up
Solving (d): Create the categories
Based on the calculated parameters above, the categories are: <em>7 - 10, 11 - 14, 15 - 18, 19 - 22 and 23 - 26</em>
Solving (e): The histogram
First construct the frequency table
Intervals ---- Frequency --- Midpoint
7 - 10 --------- 2 ---------------- 8.5
11 - 14 ---------- 2 ----------------- 12.5
15 - 18 -------- 5 ----------------- 16.5
19 - 22 -------- 7 ------ ----------- 21.5
23 - 26 ---------- 3 ----------------- 24.5
The midpoint is calculated by calculating the mean of the intervals.
For instance:
For class 7 - 10, the midpoint is: (7+10)/2 = 17/2= 8.5
This is applied to other classes too
The midpoint is then plotted against the frequency.
See attachment