Comparing Measures of Center and Variability — Quiz Answers

Daniela recorded the low temperatures during the school day last week and this week. Her results are shown in the table. Low Temperatures during the School Day This Week and Last Week Low Temperatures This Week degree cap f 42 38 45 46 39 Low Temperatures Last Week degree cap f 56 58 52 62 62 Daniela used the steps below to find a relationship between the difference in the mean temperatures and the mean absolute deviations of the data sets. This Week Last Week Step 1 Find the mean. the fraction with numerator 42 plus 38 plus 45 plus 46 plus 39 and denominator 5 is equal to 42 Find the mean. the fraction with numerator 56 plus 58 plus 52 plus 62 plus 62 and denominator 5 is equal to 58 Step 2 Find the mean absolute deviation. the fraction with numerator start absolute value 42 minus 42 end absolute value plus start absolute value 38 minus 42 end absolute value plus start absolute value 45 minus 42 end absolute value plus start absolute value 46 minus 42 end absolute value plus start absolute value 39 minus 42 end absolute value and denominator 5 is equal to 2 point 8 Find the mean absolute deviation. the fraction with numerator start absolute value 56 minus 58 end absolute value plus start absolute value 58 minus 58 end absolute value plus start absolute value 52 minus 58 end absolute value plus start absolute value 62 minus 58 end absolute value plus start absolute value 62 minus 58 end absolute value and denominator 5 is equal to 3 point 2 Step 3 Find the ratio of the differences of the means compared to the mean absolute deviation. 42 over 2 point 8 is equal to 15 Find the ratio of the differences of the means compared to the mean absolute deviation. (58)/(3.2)=18.1⁢.25 Step 4 The difference in the means is about the fraction with numerator 15 plus 18 and denominator 2 is equal to 16 point 5 times the mean absolute deviations. In which step did Daniela make the first error?

The means and mean absolute deviations of the individual times of members of two relay swim teams are shown in the table. Means and Mean Absolute Deviations of Individual Times of Members of 4 times 200 –meter Relay Swim Teams Team A Team B Mean 127 point 9 s 127 point 4 s Mean Absolute Deviation 0 point 2 6 s 0 point 2 3 s The difference of the means is found and then compared to each of the mean absolute deviations. Which is true?

Theo recorded the means and mean absolute deviations of his language arts and Biology scores. He found the difference in the means of the scores of the two subjects. What is the approximate ratio of the difference in the means to each of the mean absolute deviations? Means and Mean Absolute Deviations of Theo’s Scores Language Arts Biology Mean 98 90 Mean Absolute Deviation 3 point 5 5

The means and mean absolute deviations of the individual times of members on two 4 times 400 –meter relay track teams are shown in the table. Means and Mean Absolute Deviations of Individual Times of Members of 4 times 400 –meter Relay Track Teams Team A Team B Mean 59 point 3 2 s 59 point 1 s Mean Absolute Deviation 1 point 5 s 2 point 4 s What is the ratio of the difference in the means of the two teams to the mean absolute deviation of Team B?

Two months ago, the mean daily rainfall in a local city was 9 point 4 cm. The mean absolute deviation was 3 point 5 cm. Last month, the mean daily rainfall in that city was 11 point 5 cm, and the mean absolute deviation was 1 point 6 cm. Which statement about the rainfall is true?

The means and mean absolute deviations of the amount of rain that fell each day in a local city, last week and this week, are shown in the table. Means and Mean Absolute Deviations of Rainfall Last Week and This Week Last Week This Week Mean 19 point 7 cm 19 point 3 cm Mean Absolute Deviation 4 point 6 cm 5 point 2 cm The difference in the mean rainfall is approximately what percent of the mean absolute deviation of the this week’s rainfall?

Souta wants to compare the mean of his test scores in French class to the mean absolute deviation. Language Test Scores French Scores 76 62 94 80 He uses the following steps to find both the mean and mean absolute deviation. French Scores Step 1 Add the scores. 76 plus 62 plus 94 plus 80 is equal to 312 Step 2 Divide the sum of the scores by 4 312 divided by 4 is equal to 78 Step 3 Add the differences between the mean and each score. open paren 76 minus 78 close paren plus open paren 62 minus 78 close paren plus open paren 94 minus 78 close paren plus open paren 80 minus 78 close paren is equal to 0 Step 4 Divide by 4 0 fourths is equal to 0 In which step did Souta make the first error?

Polina’s math scores are shown in the table. Polina’s Math Scores Math Scores 72 65 75 88 90 What is the mean absolute deviation of her math scores?

Elias likes to read during his summer breaks. The table shows the number of pages in each book he read last summer and the number of pages in each book he read this summer. Number of Pages Elias Read during the Summer Last Summer 140 220 190 180 190 This Summer 150 170 150 190 180 Which statement comparing the modes to the ranges is true?

Darius and Barb are playing a video game in which the higher score wins the game. Their scores are shown. Darius’s scores: 96, 54, 120, 87, 123 Barb’s scores: 92, 98, 96, 94, 110 Barb says that she is the winner. Darius says that it is a tie. Who is correct?