Answer to Question #347794 in Statistics and Probability for Vales

Question

A. Find (a) the mean, (b) the median, (c) the mode, and (d) the midrange.

High Temperatures. The reported high temperatures (in degrees Fahrenheit) for selected world

cities on an October day are shown below. Which measure of central tendency do you think best

describes these data?

62 42

76 38

66 91

79 66

83 77

61 90

62 74

85 63

72 64

64 68

74 42

71

Answer 1

$$62,42,76,38,66, 91,79, 66,83, 77,61, 90,$$

$$62, 74,85, 63,72, 64,64, 68,74, 42,71$$

Arrange in ascending order

$$38,42,42,61,62,62,63,64,64,66,66,68,$$

$$71,72,74,74,76,77,79,83,85,90,91$$

(a)

$$mean=\dfrac{1}{23}(38+42+42+61+62+62+63$$

$$+64+64+66+66+68+71+72+74+74$$

$$+76+77+79+83+85+90+91)$$

$$=\dfrac{1570}{23}$$

(b)

$$median=68\ (12^{th} \ place)$$

(c)

$$mode=62, 42, 64, 66, 74,$$

each appeared 2 times

(d)

$$midrange=\dfrac{38+91}{2}=64.5$$