SUBJECT:

SHD 1713: STATISTIC 1

LECTURER:

DR, LOW HOCK HENG

PREPARED BY:

NOOR AZNEE BINTI JUNAIDI ZULFADLY BIN SAIFUL MOHD RASYDUDDIN BIN MAT NAWI MOHD HAZRUL AZEWAN MOHD ASRI BIN MOHD ARIFIN MOHD FAKERRYIKMAL BIN KAMALUDIN 820423-12-5184 870314-56-5549 830503-03-5829 810406-01-5451 750203-08-5159 890417-59-5265 SX110698HDS04 SX110718HDS04 SX110686HDS04 SX105341HDD04 SX112315HDF04 SX112317HDF04

1.

A researcher has collected data on a sample of 2,000 eels in Pacific Ocean. The researcher measured the length of those eels and develops the following relative distribution: Class Length (cm) 25 to less than 30 30 to less than 35 35 to less than 40 40 to less than 45 45 to less than 50 50 to less than 55 55 to less than 60 Relative Frequency, fi 0.22 0.15 0.25 0.24 0.06 0.05 0.03

Develop a frequency distribution from the data above. Calculate the mean as weel.

Answer:

Class Length (cm) 25 to less than 30 30 to less than 35 35 to less than 40 40 to less than 45 45 to less than 50 50 to less than 55 55 to less than 60 Total

Midpoints, m 27.5 32.5 37.5 42.5 47.5 52.5 57.5

Frequency, f 440 300 500 480 120 100 60 2000

Relative Frequency, fi 0.22 0.15 0.25 0.24 0.06 0.05 0.03 1

Percentage 22 15 25 24 6 5 3 100

mf 12100 9750 18750 20400 5700 5250 3450 75400

c

∑m f

Mean from a frequency distribution , X =

j=1

j j

n

= 75400 2000

X = 37.7

2.

A randomly collected data of time taken (in minutes) to conduct test on a car engine are as follows: 141 158 165 172 188 146 159 166 172 189 141 160 166 164 179 142 151 167 175 180 142 150 160 175 180 143 152 160 172 185 143 152 160 174 200 143 154 160 176 234 148 155 160 176 255

Draw a box plot from the data above Answer

141 150 160 167 179 141 151 160 172 180 142 152 160 172 180 142 152 160 172 185 143 154 160 174 188 143 155 164 175 189 143 158 165 175 200 146 159 166 176 234 148 160 166 176 255

X smallest = 141 Position of Q1 = (n + 1) = 45+1 = 11.5 position of ranked data 4 4 So, Q1 = 151+152 = 151.5 2 Position of Q2 = (n + 1) = 45+1 = 23 position of ranked data 2 2 So, Q2 = median = 160 Position of Q3 = 3(n + 1) = 3(45+1) = 34.5 position of ranked data 4 4 So, Q3 = 175+176 = 175.5 2 X largest = 255

Case Processing Summary Cases Valid N time taken in minutes 45 Percent 100.0% N 0 Missing Percent .0% N 45 Total Percent 100.0%

The boxplot is interpreted as follows: • The box itself contains the middle 50% of the data. The upper edge (hinge) of the box indicates the 75th percentile of the data set, and the lower hinge indicates the 25th percentile. The range of the middle two quartiles is known as the inter-quartile range. The line in the box indicates the median value of the data. If the median line within the box is not equidistant from the hinges, then the data is skewed. The ends of the vertical lines or "whiskers" indicate the minimum and maximum data values, unless outliers are present in which case the whiskers extend to a maximum of 1.5 times the inter-quartile range. The points outside the ends of the whiskers are outliers or suspected outliers.

• • •

•

Top 50% of the group (28 tests) which consume about more than 160 minutes time to conduct test on the car engine. They are presented by everything above the median (the black line). Those in the top 25% of time to conduct test on the car engine (10 tests) are the shown by the top whisker and the dot and star which is 175 minutes and above. Dot and star represent those tests consume more time than normal tests (outliers). From the box plot figure, we can say that the shape of distribution is right skewed which is the value of median is larger than mean.

3.

A farmer wanted to determine whether there exist any relationship between the circumference of a pumpkin (in centimetres) and its weight (in kilograms). He collected a set of data as follows:

Circumference (cm) 50.0...