Answer to Question #276805 in Statistics and Probability for She

Question

Find the measure of central tendency.

1. The following table displays the age of female actors when they starred in their Oscar-winning best actor performance.

Age of best female actors award recipients, academy awards, 1980-2015

41 33 31 74 33 49 38 61 21 41 26 80

42 29 33 36 45 49 39 34 26 25 33 35

35 28 30 29 61 32 33 45 66 25 46 55

2. The following table displays the ages of male actors when they starred in their Oscar-winning best actor performance.

Age of best female actor award recipients, academy awards 1980-2015

40 42 37 76 39 53 45 36 62 43 51 32

42 54 52 37 38 32 45 60 46 40 36 47

29 43 37 38 45 50 48 60 43 58 46 33

Answer 1

1.

$$21,25,25,26,26,28,29,29,30,31,32,33,$$

$$33,33,33,33,34,35,35,36,38,39,41,41,$$

$$42,45,45,46,49,49,55,61,61,66,74,80$$

$$n=36, \sum_ix_i=1439$$

$$mean=\dfrac{1}{n}\sum_ix_i=\dfrac{1439}{36}\approx39.9722$$

$$median=\dfrac{35+35}{2}=35$$

$$mode=33 \text{ \ \ appeared 5 times}$$

2.

$$29,32,32,33,36,36,37,37,37,38,38,39,$$

$$40,40,42,42,43,43,43,45,45,45,46,46,$$

$$47,48,50,51,52,53,54,58,60,60,62,76$$

$$n=36, \sum_ix_i=1615$$

$$mean=\dfrac{1}{n}\sum_ix_i=\dfrac{1615}{36}\approx44.8611$$

$$median=\dfrac{43+43}{2}=43$$

$$mode=37,43,45 \text{ \ \ each appeared 3 times}$$