9.5 Independent Practice

A basketball player recorded the number of points she scored in her last 5 games.

• She scored a different number of points in each game.

• The mean of the number of points scored was 22.

• The median of the number of points scored was 20.

Based on this information, select the two statements that MUST be true.

• In more than half the games, the player scored 20 or greater.

• The player scored 20 points in at least one game.

• The player scored 22 points in at least one game.

• The player did not score less than 20 points.

• In more than half the games, the player scored 22 or greater.

Answer explanation

Since the median is 20, at least three scores must be 20 or greater. Thus, more than half the games had scores of 20 or greater. The player must have scored 20 points in at least one game to achieve this median since there are an odd number of scores.

Deb recorded the number of cups of water she drank each day for 7 days.

• The median daily number of cups she drank was 6.

• The range of the number of cups she drank was 4.

Which statement can be made from the given information?

• On at least one day, Deb drank exactly 6 cups of water.

• The least amount of water Deb drank could have been 1 cup.

• The mean daily number of cups of water Deb drank is greater than the median daily number of cups of water.

• If the least amount of water Deb drank was 3 cups, then the greatest amount of water she drank was 9 cups.

Answer explanation

Since the median is 6, at least one of the 7 daily amounts must be 6. The range of 4 means the highest and lowest values differ by 4, but this does not affect the presence of 6 in the data.

A group of wildlife researchers were analyzing the mean and median lengths of 7 fish their team had observed. The fish all had different lengths between 15 cm and 33 cm.

One of the researchers found out they were misreading the shortest length. It was actually 12 cm, not 15 cm. How will this length decrease affect the mean and median?

• Both the mean and median will decrease.

• The mean will decrease, and the median will stay the same.

• The mean will decrease, and the median will increase.

• The mean will stay the same, and the median will decrease.

Answer explanation

The mean will decrease because the shortest length is now lower, affecting the average. The median, being the middle value, remains unchanged since the new shortest length does not alter the order of the lengths.

The table shows the number of minutes Carol and Anna walked each day for 5 days. Determine whether the statement is true or false.

Anna’s mean for the number of minutes she walked is greater than Carol’s mean.

• True

• False

Answer explanation

To find the means, add the minutes walked by Anna and divide by 5, then do the same for Carol. If Anna's total is higher, her mean will be greater. The calculations show Anna's mean is indeed greater than Carol's, making the statement true.

The table shows the number of minutes Carol and Anna walked each day for 5 days. Determine whether the statement is true or false.

Carol’s mean for the number of minutes is equal to her median.

• True

• False

Answer explanation

To find Carol's mean, sum her walking minutes and divide by 5. For the median, arrange her minutes in order and find the middle value. If both calculations yield the same result, the statement is true, which it is.

The table shows the number of minutes Carol and Anna walked each day for 5 days. Determine whether the statement is true or false.

Anna’s median for the number of minutes is greater than her mean.

• True

• False

Answer explanation

To determine if Anna's median is greater than her mean, we calculate both. If the median is less than or equal to the mean, the statement is false. In this case, Anna's mean is greater than her median, making the statement false.

A cat gave birth to 3 kittens who each had a different weight between 147 and 159 grams. Their weights are shown in the table. Then, the cat gave birth to a 4th kitten that weighed 157 grams. How will the birth of the 4th kitten affect the mean and median?

• Both the mean and median will decrease, but the median will decrease by more than the mean.

• Both the mean and median will decrease, but the mean will decrease by more than the median.

• Both the mean and median will increase, but the median will increase by more than the mean.

• Both the mean and median will increase, but the mean will increase by more than the median.

Answer explanation

The 4th kitten's weight of 157 grams is higher than the previous weights, increasing both the mean and median. Since the median is the middle value, it will increase more significantly than the mean, which is affected by all values.