Question

question #3
which number could represent the missing number in the data such that the distribution of the data is approximately normal?

61
0
32
22

Explanation:

Step1: Recall normal distribution property

A normal distribution is symmetric. The frequencies on either side of the center should be approximately equal. The first interval ($0 - 49$) has frequency $11$, the second ($50 - 99$) has $34$, the fourth ($150 - 199$) has $33$, and the fifth ($200 - 249$) has $12$.

Step2: Analyze symmetry

The sum of the frequencies of the first and fifth intervals is $11 + 12=23$. The sum of the frequencies of the second and fourth intervals is $34 + 33 = 67$. For symmetry (approximate normal distribution), the frequency of the middle ($100 - 149$) interval should balance the distribution. If we consider the pattern of frequencies increasing then decreasing, and looking at the values close to the average of the sums of pairs (but more simply, looking at the values to make the distribution bell - shaped). The value $61$ would make the distribution too skewed (as it would be much larger than other values), $0$ and $22$ are too small. The value $32$ is close to the values around it and helps in creating a bell - shaped (approximate normal) distribution.

Answer:

$32$