two sets of data are shown. data set a: 30, 38, 42, 42, 43, 47, 51, 51, 57, 59 data set b: 38, 39, 40, 42…

two sets of data are shown. data set a: 30, 38, 42, 42, 43, 47, 51, 51, 57, 59 data set b: 38, 39, 40, 42, 44, 46, 47, 50, 51, 52 choose all the measures which are greater for data set a than for data set b. mean range median standard deviation interquartile range

two sets of data are shown. data set a: 30, 38, 42, 42, 43, 47, 51, 51, 57, 59 data set b: 38, 39, 40, 42, 44, 46, 47, 50, 51, 52 choose all the measures which are greater for data set a than for data set b. mean range median standard deviation interquartile range

Answer

Explanation:

Step1: Calculate mean of Data Set A

$\text{Mean}_A=\frac{30 + 38+42+42+43+47+51+51+57+59}{10}=\frac{460}{10} = 46$

Step2: Calculate mean of Data Set B

$\text{Mean}_B=\frac{38+39+40+42+44+46+47+50+51+52}{10}=\frac{449}{10}=44.9$

Step3: Calculate range of Data Set A

$\text{Range}_A=59 - 30=29$

Step4: Calculate range of Data Set B

$\text{Range}_B=52 - 38 = 14$

Step5: Calculate median of Data Set A

Arrange in order: 30, 38, 42, 42, 43, 47, 51, 51, 57, 59. Median is $\frac{43 + 47}{2}=45$

Step6: Calculate median of Data Set B

Arrange in order: 38, 39, 40, 42, 44, 46, 47, 50, 51, 52. Median is $\frac{44+46}{2}=45$

Step7: Calculate standard - deviation of Data Set A

  1. Calculate the variance. First, find the differences from the mean: $(30 - 46)^2=256,(38 - 46)^2 = 64,(42-46)^2=16,(42 - 46)^2=16,(43 - 46)^2 = 9,(47-46)^2=1,(51 - 46)^2=25,(51 - 46)^2=25,(57 - 46)^2=121,(59 - 46)^2=169$ Variance $s_A^2=\frac{256+64 + 16+16+9+1+25+25+121+169}{10}=\frac{702}{10}=70.2$ Standard - deviation $s_A=\sqrt{70.2}\approx8.38$
  2. Calculate the variance of Data Set B. Differences from the mean: $(38 - 44.9)^2=47.61,(39 - 44.9)^2=34.81,(40 - 44.9)^2=24.01,(42 - 44.9)^2=8.41,(44 - 44.9)^2=0.81,(46 - 44.9)^2=1.21,(47 - 44.9)^2=4.41,(50 - 44.9)^2=26.01,(51 - 44.9)^2=37.21,(52 - 44.9)^2=50.41$ Variance $s_B^2=\frac{47.61+34.81+24.01+8.41+0.81+1.21+4.41+26.01+37.21+50.41}{10}=\frac{234.9}{10}=23.49$ Standard - deviation $s_B=\sqrt{23.49}\approx4.85$

Step8: Calculate inter - quartile range of Data Set A

  1. First, find the first quartile $Q_1$ and third quartile $Q_3$. The ordered data set is 30, 38, 42, 42, 43, 47, 51, 51, 57, 59. The lower half is 30, 38, 42, 42, 43. $Q_1 = 42$ The upper half is 47, 51, 51, 57, 59. $Q_3=51$ Inter - quartile range $IQR_A=Q_3 - Q_1=51 - 42 = 9$
  2. For Data Set B, the ordered data set is 38, 39, 40, 42, 44, 46, 47, 50, 51, 52. The lower half is 38, 39, 40, 42, 44. $Q_1 = 40$ The upper half is 47, 50, 51, 52. $Q_3=50.5$ Inter - quartile range $IQR_B=Q_3 - Q_1=50.5 - 40 = 10.5$

Answer:

mean, range, standard deviation