Answer:
[tex]Range = 17[/tex]
[tex]Intervals = 5[/tex]
[tex]Widt = 4[/tex]
Step-by-step explanation:
Given
The above data
Solving (a): The range:
[tex]Range = Highest - Least[/tex]
Where
[tex]Highest = 24[/tex]
[tex]Least = 7[/tex]
So:
[tex]Range = 24 - 7[/tex]
[tex]Range = 17[/tex]
Solving (b): Number of intervals.
From the given data:
[tex]n = 25[/tex]
[tex]Intervals = \sqrt n[/tex]
[tex]Intervals = \sqrt {25[/tex]
[tex]Intervals = 5[/tex]
Solving (c): Interval width
This is calculated as:
[tex]Width = \frac{Range}{Intervals}[/tex]
[tex]Width = \frac{17}{5}[/tex]
[tex]Width = 3.4[/tex]
[tex]Widt = 4[/tex] --- round up
Solving (d): Create the categories
Based on the calculated parameters above, the categories are: 7 - 10, 11 - 14, 15 - 18, 19 - 22 and 23 - 26
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
