Question

A survey of enrollment at 35 community colleges across the United States yielded the following figures†.

6414; 1550; 2109; 9350; 21828; 4300; 5944; 5722; 2825; 2044; 5481; 5200; 5853; 2750; 10012; 6357; 27000; 9414; 7681; 3200; 17500; 9200; 7380; 18314; 6557; 13713; 17768; 7493; 2771; 2861; 1263; 7285; 28165; 5080; 11622

• Part (a)

  Organize the data into a chart with five intervals of equal width.

  Enrollment	Frequency
  0 - 6,000
  6,001 - 12,000
  12,001 - 18,000
  18,001 - 24,000
  24,001 - 30,000

• Part (b)

  Construct a histogram of the data.

• Part (d)

  Calculate the sample mean. (Round your answer to one decimal place.)
  students

• Part (e)

  Calculate the sample standard deviation. (Round your answer to one decimal place.)
  students

• Part (f)

  A school with an enrollment of 3,700 would be how many standard deviations away from the mean? (Round your answer to two decimal places.)
  standard deviations

Answer 1

Solution: The data given in the question statement is as below. Computing an additional column Sr. No Enrolment 6414 1550 2109 9350 21828 4300 5944 5722 2825 2044 5481 5200 5853 2750 10012 6357 27000 9414 7681 3200 17500 4905085.92 50108600.44 42507046.92 520211.87 174220389.12 18738014.72 7207844.21 8449154.04 33683431.15 43358838.49 9908285.09 11756277.58 7704748.41 34559617.58 1913400.32 5160815.61 337503089.01 616628.78 898216.52 29471249.01 78699203.29 4 6 8 9 10 12 13 14 15 16 17 18 19 20 21

Part-B: Histogram 18 16 14 12 10 8 6 4 2 0 16 12 3 2 0-6000 6001-12000 12001-18000 18001-24000 24001-30000 Part-D: Samplem 302006=8628.7

Part-E: Sample standard deviation: Σ(x _が V n-1 1163939609869 35 1 = 6943.9 Part-F: Let an enrolment of 3,700 would be k standard deviations away from the mean an700-8628.7-=-0.71 3700 8628.7 6943.9 Hence, an enrolment of 3,700 would be -0.71 standard deviations away from the mean