Math 223 F18 Sections 2.3 and 2.4 Name: For problems 1-2 below, determine if the

Question

Math 223 F18 Sections 2.3 and 2.4 Name: For problems 1-2 below, determine if the corresponding statements are TRUE or FALSE and circle the Consider the histogram of hourly incomes given below: Hedogran of Haurty Income 1. The mean hourly income is larger than the median hourly income. TRUE FALSE 2. This histogram is skewed to the left. TRUE FALSE 3. Construct a data set of size 6 where the deviations are -6,-2,-1, 0, 4, 5. Construct a data set of size 8 where the mean and the median are both 85. Note: ALL eight numbers must be DIFFERENT. 4.

Explanation / Answer

1. True.

Since the most of the data values concentrated on the left side , so thet mean is greater than median.

2. False.

If we obtained the smooth curve for this histogram then we get the tailed elongated in right side

So. the given distribution is positively skewed.

Suppose the mean of the dataset is 10

Then the deviation = 0 from the mean is x - mean = 0

so that x - 10 = 0

x = 10

So for deviation 0, we get the data value = 10

Now take deviation = -6

x - mean = -6

x = 10 - 6 = 4

for deviation = -2

x = 10 - 2 = 8

for deviation = -1

x = 10 - 1 = 9

for deviations 4 and 5,

x = 10 + 4 = 14 and x = 10+5 = 15

So we get the data set as 4, 8, 9, 10, 14, 15

4 ) Take the 4th and fifth value of the dataset are 84 and 86 respectively

Then obtained the first three values as

first value = 84 - 3 = 81

2nd value = 84 - 2 = 83

3rd value = 84 - 1 = 83

6th value = 86 + 1 = 87

7th value = 86 + 2 = 88

8th value = 86 + 3 = 89

So the required dataset is 81, 82, 83, 84, 86, 87, 88, 89

Note that we can construct many dataset whose mean and median are equal to 85 .

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