Amissing data value from a set of data has a z-score of –2.1. fred already calculated the mean and standard deviation to be u=43 and o=2 . what was the missing data value? round the answer to the nearest whole number.

a)39

b)41

c)45

d)47

Answer-

The missing data value is 39.

Solution-

We know that a Z-score is the number of standard deviations from the mean a data point is. Mathematically it is represented as,

Where,

Z = Z-score or standard score,

X = Raw score,

μ = Mean of the sample

σ = Standard deviation

Here, we are given with

Z-score = -2.1

μ = 43

σ = 2

So the raw score or X is missing here, putting the values in teh formula,

A) 39

Step-by-step explanation:

For any random variable x , the formula to find the z-score is given by :-

Given : A missing data value from a set of data has a z-score of –2.1.

Fred already calculated the mean and standard deviation to be and .

Substitute all the value in the formula , we get

Multiply 2 both sides , we get

Add 43 on both the sides , we get

Or

Hence, the missing data value = 39