2.5 Using Measures of Central Tendency

Given the frequency table below for a list of recorded lengths (in inches) of randomly sampled garden snakes, find the mean. V - F 9 -8 10 -3 11 - 2 12 - 2 13 - 1 14 - 1 15 - 3

Mean 11 inches Remember that the mean is the sum of all the numbers divided by the number of numbers. The frequency table tells you the number of time that each number appears in the set of data. So to get the sum of all the numbers in the set of data, we take each frequency multiplied by its value and add them all up: Sum=9⋅8+10⋅3+11⋅2+12⋅2+13⋅1+14⋅1+15⋅3=72+30+22+24+13+14+45=220 The number of numbers in the list is the sum of the frequencies. Number of numbers=8+3+2+2+1+1+3=20 So the mean of the recorded lengths (in inches) of randomly sampled garden snakes is Sum divided by Number of numbers 220/20=11

3. Elliot likes to find garden snakes in his backyard and record their lengths. Estimate the mean of the lengths (in inches) of the garden snakes given in the following grouped frequency table.Round the final answer to one decimal place.

Mean 11.5

Given the following list of minutes randomly selected customers waited in line to buy tickets for a play, find the median. 17,11,34,22,4,9,12,31,21,15

Median 16 It helps to put the numbers in order. 4,9,11,12,15,17,21,22,31,34 Now, because the list has length 10, which is even, we know the median number will be the average of the middle two numbers, 15 and 17. So the median number of minutes randomly selected customers waited in line to buy tickets for a play is 16.

Given the following list of data, find the median. 22,33,17,8,17,29,18,13,26,28

Median 20 It helps to put the numbers in order. 8,13,17,17,18,22,26,28,29,33 Now, because the list has length 10, which is even, we know the median number will be the average of the middle two numbers, 18 and 22. So the median is 20.

Given the following list of tips (in dollars) earned in the last hour by waiters in a Japanese restaurant, find the median. 30,17,47,47,26,17,36,31,21,17

Median 28 Dollars It helps to put the numbers in order. 17,17,17,21,26,30,31,36,47,47 Now, because the list has length 10, which is even, we know the median number will be the average of the middle two numbers, 26 and 30. So the median amount of tips (in dollars) earned in the last hour by waiters in a Japanese restaurant is 28.

Find the median of the following list of inches traveled by randomly selected worms in a two minute time period. 11,7,5,12,20,6

Median = 9 inches It helps to put the numbers in order. 5,6,7,11,12,20 Now, because the list has length 6, which is even, we know the median number will be the average of the middle two numbers, 7 and 11. So the median number of inches traveled by randomly selected worms in a two minute time period is 9.

Find the mode of the following amounts (in thousands of dollars) in checking accounts of randomly selected people aged 20-25. 2,4,4,7,2,9,9,2,4,4,11

Mode = 4

A surveyor would like to find the mean number of pets living in apartments in a city. He collects data from 36 apartments in the area. The graph shows the frequency for the number of pets living in the apartments. Find the mean number of pets living in the 36 city apartments, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.

The frequency graph shows the frequency for each data value. So, we can compute the mean by added up all the data values and dividing by the total number of data values. 13⋅1+11⋅2+9⋅3+2⋅4+1⋅5+0⋅6+0⋅736=7536≈2.08. Rounding to the nearest tenth, we have the mean is 2.1.

A cashier would like to find the mean number of dairy products purchased per customer at a grocery store. He collects data from 53 people checking out at the grocery store. The graph shows the frequency for the number of dairy products purchased. Find the mean number of dairy products purchased for the 53 customers, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.

mean 3.9

A student would like to find the mean number of people living in households in a neighborhood. She collects data from 65 homes in the area. The graph shows the frequency for the number of people living in the homes.Find the mean number of people living in the 65 homes, and round your answer to the nearest tenth. Record your answer by dragging the purple point to the mean.

mean 4.9

Estimate the mean of the number of pull-ups completed by students during a gym class given in the following grouped frequency table. Round the final answer to one decimal place. Value Interval - Frequency 2-5 - 11 6-9 - 6 10-13 - 3

mean estimate = 5.9 pull-ups

Find the mode of the following number of countries randomly selected travelers visited in the past two years. 13,13,15,7,8,4,4,7,13

mode 13