Question

Directions: Solve the following problems.

Jimmy’s family moved to a tropical climate. For the year that followed, he recorded the number of days that had a temperature above 400C each month. His data contained -

14, 14, 10, 12, 11, 13, 11, 11, 14, 10, 13 and 8

1) Find the mean for his data set of days that had a temperature above 400C.

2) Find the median for his data set of days that had a temperature above 400C.

3) Find the mode for his data set of days that had a temperature above 400C.

4) If, instead, there are 5 more days per month that had a temperature above 400C, what will be the mean for the data?

5) If, instead, there are 2 more days per month that had a temperature above 400C, what will be the mode for the data?

6) If the number of days per month that had a temperature above 400C, doubles each month in that year, what will be the median for the data?

7) For what value of x will 9, 16, and x have the same mean (average) as that of 26 and 12?

8) For what value of x will 55 and x have the mean (average) as 67?

9) The mean (average) weight of three boys is 40 pounds. One of the boys weighs 50 pounds. The other two boys have the same weight. Find the weight of each of the boys?

10) A cat consumes 2 cups of milk every day. How much milk does that cat drink on average in a week? What is the mode for the question above?

Answer 1

To find the mean of Jimmy’s data set, you need to add up all the values and divide by the number of values. The mean is:

(14 + 14 + 10 + 12 + 11 + 13 + 11 + 11 + 14 + 10 + 13 + 8) / 12 = 132 / 12 = 11

To find the median of Jimmy’s data set, you need to arrange the values in ascending order and find the middle value. If there is an even number of values, you take the average of the two middle values. The median is:

8, 10, 10, 11, 11, 11, 12, 13, 13, 14, 14, 14

The median is (11 + 12) / 2 = 11.5

The mode is the value that appears most frequently in a data set. In Jimmy’s data set, the mode is:

14 (since it appears three times)

If there are five more days per month that had a temperature above 40°C, then each value in Jimmy’s data set would increase by five. The new mean would be:

(19 + 19 + 15 + 17 + 16 + 18 + 16 + 16 +19+15+18+13)/12=17

If there are two more days per month that had a temperature above 40°C, then each value in Jimmy’s data set would increase by two. The new mode would be:

16 (since it appears three times)

If the number of days per month that had a temperature above 40°C doubles each month in that year, then the new data set would be:

14,28,56,112…

The median for this data set cannot be calculated as it is an infinite geometric sequence.

Let x be the value we are looking for. The mean of {9,16,x} is equal to the mean of {26,12}. So,

(9+16+x)/3=(26+12)/2 x=38-25 x=13

Let x be the value we are looking for. The mean of {55,x} is equal to the mean of {67}. So,

(55+x)/2=67 x=134-55 x=79

Let x be the weight of each of the other two boys. The mean weight of three boys is given as:

(50+x+x)/3=40 100+2x=120 2x=20 x=10

So each of the other two boys weighs: x =10 pounds.

A cat consumes two cups of milk every day. In a week (7 days), it will consume:

7 *2 =14 cups.

The mode for this question is not applicable since there is only one value.

Answer 2

Mean:
To find the mean, we need to sum up all the values and divide by the total number of values.
Sum of the values: 14 + 14 + 10 + 12 + 11 + 13 + 11 + 11 + 14 + 10 + 13 + 8 = 141
Total number of values: 12

Mean = Sum of values / Total number of values = 141 / 12 = 11.75

Therefore, the mean for Jimmy's data set is 11.75.

Median:
To find the median, we need to arrange the values in ascending order and find the middle value.
Arranged data set: 8, 10, 10, 11, 11, 11, 12, 13, 13, 14, 14, 14

Since there are 12 values, the median will be the average of the two middle values:
Median = (11 + 12) / 2 = 11.5

Therefore, the median for Jimmy's data set is 11.5.

Mode:
The mode is the value that appears most frequently in the data set.
In Jimmy's data set, the mode is 11 and 14 because they both appear 3 times, more than any other value.

Therefore, the mode for Jimmy's data set is 11 and 14.

Mean with 5 more days per month:
If we add 5 more days to each month, the data set will become:
19, 19, 15, 17, 16, 18, 16, 16, 19, 15, 18, 13
To find the new mean, we calculate the sum of the new values and divide by the total number of values:

Sum of the new values: 19 + 19 + 15 + 17 + 16 + 18 + 16 + 16 + 19 + 15 + 18 + 13 = 201
Total number of values: 12

Mean = Sum of new values / Total number of values = 201 / 12 = 16.75

Therefore, the mean for the new data set is 16.75.

Mode with 2 more days per month:
If we add 2 more days to each month, the data set will become:
16, 16, 12, 14, 13, 15, 13, 13, 16, 12, 15, 10
To find the new mode, we identify the value that appears most frequently in the new data set.

In the new data set, the mode is 13 because it appears 3 times, more than any other value.

Therefore, the mode for the new data set is 13.

Median when the number of days doubles each month:
If the number of days per month doubles each month, the data set will become:
28, 28, 20, 24, 22, 26, 22, 22, 28, 20, 26, 16
To find the new median, we arrange the values in ascending order and find the middle value.

Arranged data set: 16, 20, 20, 22, 22, 22, 24, 26, 26, 28, 28, 28

Since there are 12 values, the median will be the average of the two middle values:
Median = (22 + 24) / 2 = 23

Therefore, the median for the new data set is