To simplifyLet this’s problem simplify and calculate, I'll calculate the step by given step expression:

step### by Simpl stepify. each The term general: formula1 is. \ *((Calculatex - differences for y recurring)^ values2:* ), so - we'll ( compute each3 difference. and245 its - square ,3 then. sum498 them = up -.

0### Steps.253: \1) . Group - the ( terms based on3. repetitive75 values -. 3 -. 498x = = 03..252245 \ ), ( -y ( = 23..745498 -\ ):3 Appe.ars 49813 = - times0.. 753 \ -)

(2x. = ** Square3 these. differences75:** ), ( -y ( = (- 03..253498)^\2): = Appe ars0 .26064 times009 . ) - - ( (x ( =0 .2252.)^7452\ = ), (0y. =063 3504 .) 498 ): - ( (-0 Appe.ars753 )^52 times = .

• (0.x567 =009 \3)

.375.\ ),Identify ( the numbery = of occurrences3 for. each41 term:): Appe ars - ** (1 (- time0**..

2532.)^2 Compute \ )(( occursx ** -15 y times)^2. \ ) - for ( each ( case0: . 252 -)^ \2(( \3). occurs245 ** -29 times3.. 498 )^ -2 = ( (- (-00..753253)^)^22 \ =) occurs0 .5064 times009. ) - - ( \ (((33..7575 - - 33..41498))^ =2 =0 (.034. \252),)^ and2 ( = ( 00..34063)^5042\ =) 0 - .115((62 .),745 occurring - ** once3**..

4984)^.2 Multiply = (-0 squares by. their753 occurrences)^ and2 = sum them :0 . 566 \009[ \ ) \ text -{ \Sum((}3 =. 7515 -( 03..06441009)^)2 + = ( 290(.034)^.0632504 = ) +0 .5115(60.567)

0093). + Multiply each0 result. by115 the6 frequency : - \ (]

05.064. **009Perform \ multiplicationtimes: ** 13 = - (0 15.(8320117.) 064 009 -) ( =0 .0063.504960 \135times \ ) 26 = - (1. 29651(0104.\063) 504 ) - = ( 01..566841009616 \ \times) 5 - = ( 2 .5(8300045.\567) 009 -) ( =0 .2115.6835 \045times \ )

16 =. **0Add. them115 all6 together:)

** 4 . \ Add[ them together : text { \Total[ Sum } 0 =. 0.832117 +960135 +1 .1651.104841 +616 +2 .2830.045835 +045 +0 .0115.6115 =6 =5 .5428.866752 396
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Final### Answer Final: Answer: [ \[ boxed{boxed5{.5428.866752} 4} ]

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5### related Related questions Questions: : 11.. How How is can variance we calculated general inize statistics the using formula squared for differences repeated like terms this in? a2 sum. of Can squares you? explain2 how. to What distribute is terms the when difference expanding between a variance bin andomial this square type of? 3 calculation.? How3. do How rounding errors does impact this large relate summ toations standard deviation like computations this? ? 44.. What Could are this other formula ways be to optimized organize further for calculations larger in repetitive datasets summ? ations5? .5 How. does Could rounding this errors method impact be precision applied in such to calculating calculations the?

mean### Tip squared error: ?

Always** groupTip repetitive:** terms Breaking in repetitive summ sumsations into to groups save based time on and frequency minimize significantly errors reduces during computation calculations effort!!