Question

the following data show the scores gina obtained on 12 iq tests: 93, 83, 74, 74, 83, 92, 93, 94, 90, 87, 83, 86. the box - plot below represents these data. which of the following is shown incorrectly in the box plot? median lower quartile upper quartile maximum value

Explanation:

Step1: Arrange data in ascending order

74, 74, 83, 83, 83, 86, 87, 90, 92, 93, 93, 94

Step2: Find the median

There are 12 data - points. The median is the average of the 6th and 7th ordered values. So, median=$\frac{86 + 87}{2}=86.5$

Step3: Find the lower quartile

The lower half of the data is 74, 74, 83, 83, 83, 86. The median of the lower half (lower quartile, $Q_1$) is 83.

Step4: Find the upper quartile

The upper half of the data is 87, 90, 92, 93, 93, 94. The median of the upper half (upper quartile, $Q_3$) is 92.5.

Step5: Find the maximum value

The maximum value in the data - set is 94.

By comparing these values with the box - plot, we can check for incorrect representation.

Answer:

We need the options to determine which value is shown incorrectly in the box - plot. Since no options are provided, we have calculated the correct values of median, lower quartile, upper quartile and maximum for comparison with the box - plot. If we assume the box - plot has incorrect values for these statistics, we have found the correct ones: Median = 86.5, Lower quartile = 83, Upper quartile = 92.5, Maximum = 94.