The IQ scores of 50 students are given below.   118 85 110 86 109 106 110 89 106 115 107 99 91 114 112 106 89 118 90 119 101 117 111 86 86 100 115 94 112 110 106 88 86 99 102 99 109 104 115 85 94 87 102 96 106 88 97 86 106 119   (a) Construct a grouped frequency distribution for the data. Use 85-89 for the first class and use the same width for each subsequent class. Class Frequency    85   -   89    -     -     -     -     -     -    (b) Which of the following is the correct histogram for this data? 24681012IQ Score84.589.594.599.5104.5109.5114.5119.5Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(80,119.5,0,12);axes(238,2,1,null,2); fill="blue"; textabs([165,0],"IQ Score","above");line([84.5,-0.24],[84.5,0.24]); text([84.5,0],"84.5","below");line([89.5,-0.24],[89.5,0.24]); text([89.5,0],"89.5","below");line([94.5,-0.24],[94.5,0.24]); text([94.5,0],"94.5","below");line([99.5,-0.24],[99.5,0.24]); text([99.5,0],"99.5","below");line([104.5,-0.24],[104.5,0.24]); text([104.5,0],"104.5","below");line([109.5,-0.24],[109.5,0.24]); text([109.5,0],"109.5","below");line([114.5,-0.24],[114.5,0.24]); text([114.5,0],"114.5","below");line([119.5,-0.24],[119.5,0.24]); text([119.5,0],"119.5","below");textabs([0,115],"Frequency","right",90);rect([84.5,0],[89.5,12]);rect([89.5,0],[94.5,4]);rect([94.5,0],[99.5,5]);rect([99.5,0],[104.5,5]);rect([104.5,0],[109.5,9]);rect([109.5,0],[114.5,7]);rect([114.5,0],[119.5,8]);] 510152025IQ Score65758595105115125Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(80.5,119.5,0,28);axes(238,5,1,null,5); fill="blue"; textabs([165,0],"IQ Score","above");line([65,-0.56],[65,0.56]); text([65,0],"65","below");line([75,-0.56],[75,0.56]); text([75,0],"75","below");line([85,-0.56],[85,0.56]); text([85,0],"85","below");line([95,-0.56],[95,0.56]); text([95,0],"95","below");line([105,-0.56],[105,0.56]); text([105,0],"105","below");line([115,-0.56],[115,0.56]); text([115,0],"115","below");line([125,-0.56],[125,0.56]); text([125,0],"125","below");textabs([0,115],"Frequency","right",90);rect([89.5,0],[99.5,28]);rect([99.5,0],[109.5,14]);rect([109.5,0],[119.5,8]);] 24681012IQ Score65707580859095100105110115120Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(88.5,123,0,12);axes(238,2,1,null,2); fill="blue"; textabs([165,0],"IQ Score","above");line([65,-0.24],[65,0.24]); text([65,0],"65","below");line([70,-0.24],[70,0.24]); text([70,0],"70","below");line([75,-0.24],[75,0.24]); text([75,0],"75","below");line([80,-0.24],[80,0.24]); text([80,0],"80","below");line([85,-0.24],[85,0.24]); text([85,0],"85","below");line([90,-0.24],[90,0.24]); text([90,0],"90","below");line([95,-0.24],[95,0.24]); text([95,0],"95","below");line([100,-0.24],[100,0.24]); text([100,0],"100","below");line([105,-0.24],[105,0.24]); text([105,0],"105","below");line([110,-0.24],[110,0.24]); text([110,0],"110","below");line([115,-0.24],[115,0.24]); text([115,0],"115","below");line([120,-0.24],[120,0.24]); text([120,0],"120","below");textabs([0,115],"Frequency","right",90);rect([93,0],[98,12]);rect([98,0],[103,4]);rect([103,0],[108,9]);rect([108,0],[113,11]);rect([113,0],[118,7]);rect([118,0],[123,7]);] 246810121416IQ Score65758595105115125Frequency[Graphs generated by this script: setBorder(54,40,20,15); initPicture(76,125,0,16);axes(238,2,1,null,2); fill="blue"; textabs([165,0],"IQ Score","above");line([65,-0.32],[65,0.32]); text([65,0],"65","below");line([75,-0.32],[75,0.32]); text([75,0],"75","below");line([85,-0.32],[85,0.32]); text([85,0],"85","below");line([95,-0.32],[95,0.32]); text([95,0],"95","below");line([105,-0.32],[105,0.32]); text([105,0],"105","below");line([115,-0.32],[115,0.32]); text([115,0],"115","below");line([125,-0.32],[125,0.32]); text([125,0],"125","below");textabs([0,115],"Frequency","right",90);rect([85,0],[95,16]);rect([95,0],[105,10]);rect([105,0],[115,16]);rect([115,0],[125,8]);] IQ SCORE

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Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.