Question

question 21
in a grouped frequency distribution table, the bottom value in each class interval should be a multiple of the interval width.
true
false
question 22
in a grouped frequency distribution table, one interval is listed as 35 - 39. if the scores represent a continuous variable, what are the real limits for this interval?
34.5 and 39.5
35.5 and 39.5
34 and 40
35.25 and 39.25
question 23
find each value requested for the set of scores in the following frequency distribution table.
a. n
x f
b. σx
5 3
c. σx²
4 4

Explanation:

Step1: Answer Question 21

The bottom - value in each class interval does not have to be a multiple of the interval width. For example, an interval could be 7 - 12 where the width is 5 and the bottom - value 7 is not a multiple of 5.

Step2: Answer Question 22

For a continuous variable, the real limits of an interval 35 - 39 are 34.5 (lower real limit) and 39.5 (upper real limit). The lower real limit is found by subtracting 0.5 from the lower stated limit and the upper real limit is found by adding 0.5 to the upper stated limit.

Step3: Answer Question 23a

$N$ is the total number of scores. We sum the frequencies. Given scores $X = 5$ with frequency $f = 3$ and $X = 4$ with frequency $f = 4$, then $N=\sum f=3 + 4=7$.

Step4: Answer Question 23b

$\sum X$ is the sum of all scores. We calculate it as $\sum X=(5\times3)+(4\times4)=15 + 16=31$.

Step5: Answer Question 23c

$\sum X^{2}$ is the sum of the squared scores. First, we find the squared scores for each value of $X$ and multiply by their frequencies. For $X = 5$, $X^{2}=25$ and for $X = 4$, $X^{2}=16$. Then $\sum X^{2}=(25\times3)+(16\times4)=75+64 = 139$.

Answer:

Question 21: False
Question 22: 34.5 and 39.5
Question 23a: 7
Question 23b: 31
Question 23c: 139