The speeds in miles per hour of 30

cars were checked by radar. The data are as follows:
62 67 69 72 75 60 58 86 74 68
56 67 82 88 90 54 67 65 64 68
74 65 58 75 67 65 66 64 45 64
Find the upper and lower quartiles

Rewrite the list in ascending order, and then divide the list into four parts. That will tell you the quartile boundaries.

45 54 56 58 58 60 62
64 64 65 65 65 66 67 67
67 67 68 68 69 72 74 74
75 75 82 86 88 90

Q2 = 67 (divides into upper and lower halves)
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Q1 = 64 (median of lower half)
Q3 = 74 (median of upper half)

To find the upper and lower quartiles, you first need to arrange the given data in ascending order. Once the data is sorted, you can then find the values that divide the data into four equal parts.

Step 1: Arrange data in ascending order:
45 54 56 58 58 60 62 64 64 64
65 65 66 67 67 67 68 68 69 72
74 74 75 75 82 86 88 90

Step 2: Calculate the position of the quartiles:
There are 30 data points, so the first quartile will be at position (1/4)(30+1) = 7.75.
The second quartile (which is also the median) will be at position (2/4)(30+1) = 15.5.
And the third quartile will be at position (3/4)(30+1) = 23.25.

Note: Since the positions are fractional, you will need to interpolate to find the exact values.

Step 3: Find the quartile values:
The lower quartile (Q1) is the value at position 7.75. Interpolating the values at positions 7 and 8:
Q1 = 62 + 0.75 * (67 - 62) = 62 + 0.75 * 5 = 62 + 3.75 = 65.75

The upper quartile (Q3) is the value at position 23.25. Interpolating the values at positions 23 and 24:
Q3 = 74 + 0.25 * (75 - 74) = 74 + 0.25 * 1 = 74 + 0.25 = 74.25

Therefore, the lower quartile (Q1) is approximately 65.75 and the upper quartile (Q3) is approximately 74.25.