Question

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A study of the temperatures, in degrees F, of 80-year-old long-term care residents is being conducted The following data set has been collected as of today: 97.4 98.4 99.9 97.2 96.1 98.4 96.3 98.4 4. Find the mean. 5. Find the mode. 6. Find the midrange value. 7. Find the median. 8. Find the standard deviation. 9. Find the sample variance. 10. Find the CV 11. Alex has an 1Q of 100. The average IQ for his age group is 94.7 with a standard deviation of 1.9 Find the Z score.

Answer 1

Given data

97.4, 98.4, 99.9, 97.2, 96.1, 98.4, 96.3, 98.4

Arranging in ascending order we get,

{96.1, 96.3 97.2, 97.4, 98.4, 98.4, 99.9}

4) Mean = sum(Xi) / n

= (96.1+ 96.3+ 97.2+ 97.4+ 98.4+ 98.4+ 99.9)/ 7

= 97.67

5) Mode = most repeating value = 98.4 (as it is the only one which repeats twice)

6) Midrange value

= (high+low)/2

= (96.1 + 99.9)/2

= 98

7) median = 4th element of 7

= 97.4

8,9) variance = sum(Xi - x bar)/n

= {(96.1- 97.67)^2+ (96.3 - 97.67)^2+ (97.2 - 97.67)^2+ (97.4- 97.67)^2+ (98.4- 97.67)^2+ (98.4- 97.67)^2+ (99.9- 97.67)^2)/ 7

= 1.5249

standard deviation = sqrt(variance)

= sqrt(1.5249)

= 1.235

11)

u = 94.7, $\sigma$ = 1.9

x = 100

We have,

Z = (x-u)/$\sigma$

Z = (100-94.7)/1.9

Z = 2.789