Answer with explanation:
The Given data set having 5 variate arranged in ascending order = {46,78,87,89,90}
Mean of a data set
[tex]=\frac{\text{Sum of all the observation}}{\text{total number of variate in the data set}}[/tex]
Mean of the given data set
[tex]=\frac{46+78+89+87+90}{5}\\\\=\frac{390}{5}=78[/tex]
→Emi has calculated the mean Correctly which is 78.
Now to calculate variance
1. Square of Absolute difference between mean and each variate
a. | 78-46|²=32² =1024
b. | 78 - 78 |²=0²=0
c. | 89-78|²=11²=121
d. | 87-78 |²=9²=81
e. | 90-78|²=12²=144
The new data set obtained is ={ 0,81,121,144,1024}
Variance
[tex]=\frac{\text{Sum of each variate in the new data set}}{\text{Total number of variate in the data set}-1}\\\\=\frac{0+81+121+144+1024}{5-1}\\\\=\frac{1370}{4}\\\\=342.5[/tex]
Variance = 342.5
Answer:
A, Emi failed to find the difference of 89 - 78 correctly.
Step-by-step explanation:
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