Question

1. An engineer is responsible for monitoring the quality of a batch of 1000 ohm resistors. To do so, the engineer must accurately measure the resistance of a number of resistors within the batch, selected at random. The results obtained are shown below for samples 1 to 30.

1006, 1006, 978, 965, 988, 973, 1011, 1007, 935, 1045, 1001, 974, 987, 966, 1013, 960, 976, 954, 1004, 975, 1014, 955, 973, 993, 1023, 992, 981, 991, 1013 and 998.

(a) Determine the mean, median, mode, min, max and standard deviation

(b) Construct a histogram, based upon a reasonable interval width

Answer 1

For the given 30 samples 1006, 1006, 978, 965, 988, 973, 1011, 1007, 935, 1045, 1001, 974, 987, 966, 1013, 960, 976, 954, 1004, 975, 1014, 955, 973, 993, 1023, 992, 981, 991, 1013 and 998.

a) The mean is calculated as:

Mean = (1006 + 1006 + 978 + 965 + 988 + 973 + 1011 + 1007 + 935 + 1045 + 1001 + 974 + 987 + 966 + 1013 + 960 + 976 + 954 + 1004 + 975 + 1014 + 955 + 973 + 993 + 1023 + 992 + 981 + 991 + 1013 + 998)/30
= 29657/30
Mean = 988.5667

Median is the middle value of the data set which is here

The mode is the most repetitive value which is Mode = 973, 1013 both occurred twice.

the minimum value is 935 and the maximum value is 1045

The standard deviation is calculated as:

Standard Deviation σ = √(1/30 - 1) x ((1006 - 988.5667)² + ( 1006 - 988.5667)² +..................+ ( 998 - 988.5667)²)
= √(1/29) x ((17.4333)² + (17.4333)² + .....................................................................+ (9.4333)²)

= √(0.0345) x ((303.91994889) + (303.91994889) +................................. + (88.987148890001))

= √(0.0345) x (16463.3666667)

= √(567.98615000115)

= 23.8265

b)Based on the reasonable frequency table computed in excel the table is:

Class	Count
930-949	1
950-969	5
970-989	9
990-1009	9
1010-1029	5
1030-1049	1
Total=	30

Based on the frequency table the histogram is plotted below using excel as: