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Obtain the five-number summary for the given data

The test scores of 15 students are listed below.

Obtain the five-number summary for the given data The test scores of 15 students are-example-1
User Nopeva
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Answer:

B. 42, 55, 71, 87, 95

Explanation:

The five-number summary of a data set consist of the following five numbers:

  • the minimum (i.e., the smallest data point),
  • the lower/first quartile aka Q1 (i.e., the value under which 25% of the data fall when arranged in increasing numerical order),
  • the median,
  • the upper/third quartile aka Q3 (i.e., the value above which 75% of the data fall when arranged in increasing numerical order)
  • and the maximum (i.e. the largest data point).

Identifying the minimum:

42 is the smallest data point, so it's the minimum.

Identifying the median:

  • It's important (and perhaps necessary) to find the median before finding the lower and upper quartiles.
  • Before we can find the median, we must arrange the data in increasing numerical order.

Thus, we have: 42, 45, 48, 55, 56, 63, 66, 71, 73, 77, 85, 87, 90, 94, 95.

  • For a data set with an odd set of numbers, the median will have an even number.
  • We see that 71 has 7 terms to the left and right of it.

Thus, 71 is the median.

Identifying the lower/first quartile (Q1):

  • To find the lower/first quartile (Q1), we find the middle value of all the values smaller than the median.
  • Since there 7 terms smaller than 71, this middle value will also have an even number of values to the left and right of it.
  • 55 meets this requirement as it has 3 terms to the left and right of it.

Thus, the lower/first quartile (Q1) IS 55.

Identifying the upper/third quartile (Q3):

  • To find the upper/third quartile (Q3), we find the middle value of all the values larger than the median.
  • Since there are 7 terms smaller than 71, this middle value will also have an even number of values to the left and right of it.
  • 87 meets this requirement, as it has 3 terms to the left and right of it.

Thus, the upper/third quartile (Q3) IS 87.

Identifying the maximum:

95 is the largest data point, so it's the maximum.

Since B contains the numbers 42, 55, 71, 87, and 95, which we've determined are the minimum, lower/first quartile (Q1) ,the median, the upper/third quartile (Q3), and the maximum respectively, it's the answer.

User Theguy
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