Twenty five students earned the following grades on test 1. 61 99 54 96 89 71 89

Question

Twenty five students earned the following grades on test 1. 61 99 54 96 89 71 89 96 65 45 69 99 84 80 85 78 99 64 58 94 92 77 99 78 84 a)construct a relative frequency distribution. Use 40 for the first lower class limit, and class widths of 10. Class limits should be 40-49, 50-59, etc. Classes. Tallies. Frequency. Rel.Fre(round to 2 Decimal places) ---------- -------- ----------- ---------------------- ---------- -------- ---------- ----------------------- ---------- -------- ---------- --------------------- ---------- -------- ---------- ------------------------------ -------- ---------- -------------------- ---------- -------- ---------- ------------------- b)identify all class boundaries. c)identify all class midpoints. d)what percentage of students earned A's or B's, that is earned a score of 80 or higher?
Twenty five students earned the following grades on test 1. 61 99 54 96 89 71 89 96 65 45 69 99 84 80 85 78 99 64 58 94 92 77 99 78 84 a)construct a relative frequency distribution. Use 40 for the first lower class limit, and class widths of 10. Class limits should be 40-49, 50-59, etc. Classes. Tallies. Frequency. Rel.Fre(round to 2 Decimal places) ---------- -------- ----------- ---------------------- ---------- -------- ---------- ----------------------- ---------- -------- ---------- --------------------- ---------- -------- ---------- ------------------------------ -------- ---------- -------------------- ---------- -------- ---------- ------------------- b)identify all class boundaries. c)identify all class midpoints. d)what percentage of students earned A's or B's, that is earned a score of 80 or higher?
61 99 54 96 89 71 89 96 65 45 69 99 84 80 85 78 99 64 58 94 92 77 99 78 84 a)construct a relative frequency distribution. Use 40 for the first lower class limit, and class widths of 10. Class limits should be 40-49, 50-59, etc. Classes. Tallies. Frequency. Rel.Fre(round to 2 Decimal places) ---------- -------- ----------- ---------------------- ---------- -------- ---------- ----------------------- ---------- -------- ---------- --------------------- ---------- -------- ---------- ------------------------------ -------- ---------- -------------------- ---------- -------- ---------- ------------------- b)identify all class boundaries. c)identify all class midpoints. d)what percentage of students earned A's or B's, that is earned a score of 80 or higher?

Explanation / Answer

here total frequency is n=25

least score is 45 and maximum score is 99

we need to construct classes like 40-49,50-59...

so the classes should be

40-49

50-59

60-69

70-79

80-89

90-99

now within 40-49 there are values= 45 so frequency=1

in 50-59 there are values=54,58 so frequency=2

in 60-69 there are values=61,65,69,64   so frequency=4

in 70-79 there are values=71,78,77,78 so frequency=4

in 80-89 there are values=89,89,84,80,85,84 so frequency=6

in 90-99 there are values=99,96,96,99,99,94,92,99 so frequency=8

a) so frequency distribution is as follows

classes           frequency               rel. frequency(round to 2 decimal places)

40-49                     1                         1/25=0.04

50-59                     2                          2/25=0.08

60-69                     4                           4/25=0.16

70-79                     4                           4/25=0.16

80-89                     6                            6/25=0.24

90-99                     8                            8/25=0.32

b) lower class boundaries=lower class limit-(lower class limit of the next class-upper class limit of the class)/2

upper class boundaries=upper class limit+(lower class limit of the next class-upper class limit of the class)/2

so the class boundaries are

classes         lower class boundary             upper class boundary

40-49               40-(50-49)/2=39.5                     49+(50-59)/2=49.5

50-59               50-(50-49)/2=49.5                     59+(50-59)/2=59.5

60-69               60-(50-49)/2=59.5                     69+(50-59)/2=69.5

70-79               70-(50-49)/2=69.5                     79+(50-59)/2=79.5

80-89               80-(50-49)/2=79.5                     89+(50-59)/2=89.5

90-99               90-(50-49)/2=89.5                     99+(50-59)/2=99.5

c) class midpoints=(upper class boundary+lower class boundary)/2

so we have

classes         lower class boundary             upper class boundary               midpoints

40-49               40-(50-49)/2=39.5                     49+(50-59)/2=49.5             (49.5+39.5)/2=44.5

50-59               50-(50-49)/2=49.5                     59+(50-59)/2=59.5              (59.5+49.5)/2=54.5

60-69               60-(50-49)/2=59.5                     69+(50-59)/2=69.5               (69.5+59.5)/2=64.5

70-79               70-(50-49)/2=69.5                     79+(50-59)/2=79.5               (79.5+69.5)/2=74.5

80-89               80-(50-49)/2=79.5                     89+(50-59)/2=89.5                (89.5+79.5)/2=84.5

90-99               90-(50-49)/2=89.5                     99+(50-59)/2=99.5                 (99.5+89.5)/2=94.5

d) the scores with 80 or higher=89,89,84,80,85,84,99,96,96,99,99,94,92,99 (14 students)

so the percentage of students earned A's or B's=14/25*100=56% [answer]

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