Question

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 weight of each of the boys?

10) A cat consumes 2 cups of milk every day. How much milk does that cat drink on an average in a week?

11) What is mode for above question?

Answer 1

1. To find the mean of the data set, we add up all the values and divide by the total number of values:

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

2. To find the median of the data set, we need to order the values from lowest to highest and find the middle value. In this case, the middle value is the average of the two values in the middle:

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

Median = (11 + 12) / 2 = 11.5

3. The mode is the value that appears most frequently in the data set. In this case, the mode is 14 as it appears three times.

4. If there are 5 more days per month with a temperature above 400C, then we can add 5 to each value in the data set:

19, 19, 15, 17, 16, 18, 16, 16, 19, 15, 18, 13

Mean = (19 + 19 + 15 + 17 + 16 + 18 + 16 + 16 + 19 + 15 + 18 + 13) / 12 = 16.33

5. If there are 2 more days per month with a temperature above 400C, then the mode will remain the same as there are no changes in the frequencies of the values in the data set.

6. If the number of days per month that had a temperature above 400C doubles each month, the data set will look like:

14, 28, 56, 112, 224, 448, 896, 1792, 3584, 7168, 14336, 28672

The median is the middle value, which is 224.

7. To find the value of x, we need to first find the mean of 26, 12, and x:

Mean = (26 + 12 + x) / 3

We know that this mean is equal to the mean of 9, 16, and x, which is (9 + 16 + x) / 3.

Therefore, we can equate the two means and solve for x:

(26 + 12 + x) / 3 = (9 + 16 + x) / 3

26 + 12 + x = 9 + 16 + x

29 + x = 25 + x

x = 25

8. We know that the mean of 55 and x is 67:

Mean = (55 + x) / 2 = 67

Multiplying both sides by 2, we get:

55 + x = 134

x = 79

9. Let's call the weight of the two boys who weigh the same "w". We know that the mean of the three boys' weights is 40 pounds:

Mean = (50 + w + w) / 3 = 40

Simplifying the equation, we get:

100 + w = 120

w = 10

Therefore, the weight of each of the boys is 50 pounds, 10 pounds, and 10 pounds.

10. The cat consumes 2 cups of milk per day, so in a week, it drinks:

2 cups/day x 7 days/week = 14 cups/week

11. There is no mode.

Explanation:

Answer 2

10.92 days per month.

Explanation:

To find the mean, we first add up all the values in the data set: 14 + 14 + 10 + 12 + 11 + 13 + 11 + 11 + 14 + 10 + 13 + 8 = 131. Then we divide that sum by the total number of values, which is 12: 131 ÷ 12 = 10.92. Therefore, the mean for Jimmy's data set of days that had a temperature above 400C is 10.92 days per month.

Should be correct