FEMALE 295 2739 2992 3745 4486 4488 4878 4880 4881 4835 4842 6225 8680 8681 12348 14651 16767 17765 19377 19378 19382 20278 21626 32233 33104 33106 33334 33335 34779 35035 35272 35273 35505 35506 35507 35984 35988 36115 36502 38089 BMI 19.6 23.8 19.6 29.1 25.2 21.4 22.0 27.5 33.5 20.6 29.9 17.7 24.0 28.9 37.7 18.3 19.8 29.8 29.7 31.7 23.8 44.9 19.2 28.7 28.5 19.3 31.0 25.1 22.8 30.9 26.5 21.2 40.6 21.9 26.0 23.5 22.8 20.7 20.5 21.9 MALE 1391 2129 2489 2490 2738 2988 2989 3346 3606 3607 3608 3610 3747 4832 4839 5599 5600 5601 6226 7190 7192 7194 9073 9074 10864 12349 15515 16137 16521 16523 16768 17006 18392 19017 19381 19635 19991 20518 21135 32230 BMI 23.8 23.2 24.6 26.2 23.5 24.5 21.5 31.4 26.4 22.7 27.8 28.1 25.2 23.3 31.9 33.1 33.2 26.7 26.6 19.9 27.1 23.4 27.0 21.6 30.9 28.3 25.5 24.6 23.8 27.4 28.7 26.2 26.4 32.1 19.6 20.7 26.3 26.9 25.6 24.2 Laura Reid Part 1 Data Analysis ls Central tendency There are three measures of central tendency mean, median and mode. They are calculated in excel and given below in the table. MEAN MEDIA N MODE 25.74 23.9 19.6 Mean is sum of all observations divided by total number of observations. Here, mean is 25.74 implying that an average BMI of females is 25.74. The median in a series of ordered (say from low to high) values is the value at which there are just as many values less than it as there are greater than it. Here median is 23.9. So BMI of half of the females is more than 23.9 and that of other half is less than 23.9. Mode is the number occurring maximum number of times. Here mode is 19.6 implying BMI of maximum females is 19.6 Laura Reid Part 1 Data Analysis ls Measures of dispersion The three measures of dispersion namely range, standard deviation and variance is given below. range 27.2 standard deviation varianc 38.0142 e 6 Range is the difference between the maximum and minimum value. The variance and the standard deviation are both measures of the spread of the distribution about the mean. The standard deviation measures how concentrated the data are around the mean; the more concentrated, the smaller the standard deviation. Standard deviation measures spread in the same physical unit as the original data. Standard deviation and variance is given in the table above. Laura Reid Part 1 Data Analysis ls Quartiles and Interquartile range The quartiles and Interquartile range is given below Q1 Q2 Q3 IQR = Q3 - Q1 21.07 5 23.9 29.25 8.175 Outlier Any point below Q1 - 1.5*IQR and above Q3 + 1.5*IQR is considered as an outlier. The values of Q1 - 1.5*IQR and Q3 + 1.5*IQR is given below in the table. Q1 - 1.5*IQR Q3 + 1.5*IQR 8.8125 41.512 5 points below 8.8125 points above 41.5125 0 1 Hence there is only one outlier in the data. This is found with the help of conditional formatting tool in excel. The outlier is mentioned below. FEMAL E 20278 BMI 44.9 Laura Reid Part 1 Data Analysis ls Box Plot The Boxplot is an Indicator of Symmetry. If the line is close to the center of the box and the whisker lengths are the same then sample is from a symmetric population. The box plot is given below. The star in blue is the outlier. Here, BMI for females is positively skewed. That is there are very few females with high values of BMI. For a positively skewed data, mean is greater than median which is greater than mode. The same is observed from the table of central tendency. Laura Reid Part 1 Data Analysis ls Histogram The frequency distribution and corresponding histogram is given below. Count of BMI BMI 15-20 20-25 25-30 30-35 35-40 40-45 Grand Total Total 7 14 12 4 1 2 40 16 14 12 10 FREQUENCY 8 6 4 2 0 15-20 20-25 25-30 30-35 35-40 40-45 BMI I observe that distribution of BMI of females is skewed to the right. The same is observed from Box Plot and central tendency